## Lesson: Representing Data

Introducing the Concept

One of the primary reasons for representing data is to communicate information to others. Selecting how to represent that information leads to several questions, such as, “To whom are you communicating this information?” “What are the essential ideas you want to communicate?” and “What representation will best communicate those ideas?”

**Preparation:** Prepare two posters, one with data represented by a bar graph and one with data represented by a line graph. Use the graphs below.

**Prerequisite Skills and Background:** Students should be able to recognize a bar graph and a line graph and be able to make one of each, given the appropriate data.

**Say:***Today we are going to look at some graphs that you are familiar with.*(Hold up the bar graph.)*Who can tell me what kind of graph this is?*(Students should say that it is a bar graph; if they don't, remind them what it is called.)*Good. This is a bar graph showing how long five students could hold their breath.***Ask:***What specific information can you tell me about the graph?*

Students should be able to tell you how long each person held his or her breath, who held his breath the longest, who held it the shortest, and so on.**Say:***A bar graph is a good way to represent data that is made from discrete or separate quantities that you want to compare, such as the data shown above or the number of runs scored in several softball games.*

On the chalkboard, make a table using the same data as above.**Say:***Here are the same data listed in a table. Which way do you think better illustrates the data?*

Students may present arguments for both representations of the data. Some may prefer the graph because they can immediately tell who held his or her breath the longest or the shortest. Some students may prefer the table because you can readily compute differences—for example, how much longer Susan held her breath than Mourad did.**Say:***It is important to think about how you can best represent a set of data. It is also important to think whom you are going to show the data to. These are questions you will need to consider when representing data.*

Display the second poster.**Ask:***Who remembers what kind of graph this is?*(Students should say that it is a line graph. If they have forgotten, remind them that it is called a line graph.)*This graph shows how far away from home Josh was when he took his bike trip. How far away from home was he after 20 minutes?*(2 miles)**Ask:***What was the farthest Josh was away from his house?*(4 miles)*How long had Josh been riding before he started back home?*(1 hour)**Ask:***What else can you tell me from the graph?*

Students should say things like Josh rode for 2 hours, he was 3 miles from home after 40 minutes, and so on.**Say:***Line graphs are good for displaying data that vary with time, such as Josh's distance from home or the temperature over the course of a day. A line graph is a good choice if the data given are numerical and equally spaced along a continuous number scale like time.***Say:***Let's look at some different cases and see what kind of graph you would recommend for displaying the data. A class wants to make a graph of favorite subjects in school. A poll of students finds that 11 favored math, 6 favored science, 8 favored reading, and 4 favored social studies. What kind of graph would you use to show the parents on parents' night?*(a bar graph)**Ask:***What kind of graph would you use if you wanted to show the length of a tree's shadow after measuring it every hour from 9:00 a.m. to 2:00 p.m.?*(a line graph)

Write the following table on the board. Ask students to write down the information on a sheet of paper.

**Ask:***Sometimes we want to compare two data sets. For example, on the board is a table listing the amount of time that a student spends riding her bike and the time she spends reading for enjoyment each day of the week. If you wanted to show just the information about bike riding, what kind of graph would you use to represent the data?*

Students should suggest using a bar graph to show how much time is spent each day.**Ask:***Suppose you want to graph the information about reading. What kind of graph would you use?*

Again, students should say that a bar graph would be a good choice.**Say:***If you want to compare the two data sets, time spent riding and reading, you would make a***double bar graph.****Ask:***If you were to make a double bar graph, how would you label the horizontal axis?*(Days of the Week)*Good! Now, how would you label the vertical axis?*(Time in Minutes)

Show the students how to make the double bar graph. Tell students to use different colors for each data set when they draw the bars. This will make it easier to distinguish the bars representing bike riding from the bars representing reading. A key indicating which color represents reading and which color represents bike riding should be added to the graph.

Ask several questions about the double bar graph to make sure that students understand what it represents.**Ask:***On what day did this student spend the most time riding?*(Saturday)*On what day did she spend the most time reading?*(Sunday)*On what day did she spend the same amount of time reading as she spent riding?*(Friday)*On what days did she spend exactly one hour reading and riding together?*(Wednesday and Thursday)